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Question Number 120196 by ZiYangLee last updated on 30/Oct/20

$$\mathrm{The}\mathrm{ratio}\mathrm{of}\mathrm{male}\mathrm{and}\mathrm{female}\mathrm{participants}$$$$\mathrm{in}\mathrm{a}\mathrm{competition}\mathrm{is}3:2.\mathrm{Given}\mathrm{that}15\mathrm{\%}$$$$\mathrm{of}\mathrm{participants}\mathrm{are}\mathrm{prize}\mathrm{winner},\mathrm{and}\mathrm{among}$$$$\mathrm{the}\mathrm{prize}\mathrm{winner},\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{male}\mathrm{to}\mathrm{female}$$$$\mathrm{is}2:1.\mathrm{Find}\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{male}\mathrm{and}\mathrm{female}$$$$\mathrm{among}\mathrm{the}\mathrm{participants}\mathrm{that}\mathrm{are}\mathrm{not}\mathrm{prize}$$$$\mathrm{winner}.$$

Answered by benjo_mathlover last updated on 30/Oct/20

$$male:female=3:2\{\begin{array}{l}male=3k\\ female=2k\end{array}Total=5k$$$$areprizewinner=\frac{15}{100}\times 5k=\frac{3}{4}k$$$$maleprizewinner=\frac{2}{3}\times \frac{3}{4}k=\frac{1}{2}k$$$$femaleprizewinner=\frac{1}{3}\times \frac{3}{4}k=\frac{1}{4}k$$$$malenonprizewinner=3k-\frac{1}{2}k=\frac{5}{2}k$$$$femalenonprizewinner=2k-\frac{1}{4}k=\frac{7}{4}k$$$$then\frac{malenonprize}{femalenonprize}=\frac{5/2}{7/4}$$$$=\frac{5}{2}\times \frac{4}{7}=\frac{10}{7}$$

Commented by ZiYangLee last updated on 30/Oct/20

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